Simplified high frequency tuner and tuning method

ABSTRACT

An RF tuner and tuning method employs analog quadrature mixing with a coarse-stepwise tunable local oscillator to a near-baseband passband region, followed by A/D conversion of the I and Q signals, correction of phase, group delay, and amplitude errors, image rejection, and translation to baseband by (1) fixed frequency translation, (2) stepwise channelized translation, or (3) essentially continuously variable tuning over a given digital tuning range. The near-baseband passband region is sized and located such that alternating image rejection provides non-redundant and complete tuning coverage of a desired high frequency spectrum with a local oscillator step size equal to about twice the digital tuning range or about twice the number of channels digitally stepwise tunable times the channel width, effectively doubling the typical local oscillator step size. The digital tuning is preferably performed by a continuously variable bandpass decimating filter with aliasing to within R D  of baseband, where R D  is the filter&#39;s out put sampling rate, followed by fine-shifting to baseband by digital complex mixing. Demodulation is then accomplished according to signal type. 
     Image rejection and phase error and gain correction are preferably performed with a modified type III Hilbert transform pair with 90°±CF phase change and variable gain. The near-baseband passband is preferably centered at R/4 where R is the sampling rate entering the Hilbert transform.

FIELD OF THE INVENTION

This invention relates generally to devices and methods for receivingand transmitting RF signals. More particularly, this invention relatesto an especially useful device and method for receiving and tuning RFsignals, with quadrature mixing to a near baseband passband performed incontinuous-time and image rejection and translation to basebandperformed in discrete-time. The device may also be adapted to transmitRF signals if desired.

BACKGROUND OF THE INVENTION

Standard RF receiver design incorporates conversion of incoming highfrequency signals to one or more intermediate frequencies, the last ofwhich is then converted to baseband. A mixer and image rejection filterare required at each stage, resulting in complexity proportional to thenumber of stages. Such complexity is undesirable, particularly formobile communications applications where size, power consumption, andcost per unit must be minimized.

Various approaches have been taken to reduce the size, powerconsumption, and cost of receivers. One approach is to perform nearlyall of the receiver functions in the discrete-time domain in a DSP(digital signal processor) device. This results in high DSP performancerequirements and cost. Other approaches employ discrete-time processingfor baseband and for some intermediate frequency operations, reducingthe DSP performance requirements, but still requiring at least one highperformance continuous-time image rejection filter.

Direct conversion receivers offer a potential alternative for avoidingsome of the limitations of other approaches. Receivers of this typeemploy quadrature mixing directly to baseband. Discrete-time processingcan be efficiently utilized at baseband frequencies to demodulate thesignal of interest, employing the quadrature baseband signals to utilizethe entire signal spectrum centered at baseband. The complex-valuedsignal comprised of the I, Q samples allows the faithful representationof the signal of interest on both sides of baseband without distortionfrom images from opposite sides of baseband. Thus only a singlecontinuous-time frequency conversion stage need be employed. Nopreselecting bandpass filter is required to eliminate an undesiredmixing image, so that a broad tuning range is possible.

Despite the above potential advantages, direct conversion receivers alsopresent problems including: (1) 1/f noise, which dominates activedevices at low frequencies, particularly below 100 Hz, (2) time-varyingDC offsets which can saturate the later stages of the baseband signalchain, (3) products of self-mixing of strong signals which can bepresent at baseband, (4) relatively small phase and amplitude errorsbetween channels considerably reduce image rejection, and (5) fairlysharp anti-aliasing filters are required and can distort the desiredsignal if not carefully designed and precisely matched.

Attempts have been made to provide the advantages of direct conversionwithout the disadvantages by "notching out" DC from the baseband signal.This method performs well only if the signal type contains little or noinformation at or near DC. If the notch at DC is sufficiently narrow tominimize loss of information, the problems listed above related toamplification at or near DC are not eliminated.

Attempts have been made to avoid losing the information at and near DCand avoid the need for image rejection by translating a desired channelfrequency from a channelized frequency spectrum to a frequency offset asmall fixed amount from baseband, with the offset large enough to movethe DC portion of the channelized signal into a passband which excludesDC, but small enough to prevent the next adjacent channel from appearingin the passband. This technique may preserve the DC portion of thesignal, but requires sharp cut-off highpass and anti-aliasing filtersand, because of the proximity of the passband to DC, still sufferssomewhat from the other problems listed above.

SUMMARY OF THE INVENTION

In accordance with the present invention, a high frequency spectrum ofinterest is translated in continuous-time to a near-baseband passband byquadrature mixing, preferably with a coarse-tuned local oscillator,producing I and Q signals in approximate quadrature relation. The I andQ signals are then filtered in continuous-time to remove DC and toprevent unwanted aliasing upon digital conversion, and are thenconverted to digital I and Q signals.

In digital processing, various steps are performed including (1) phasecorrection (optionally including group delay correction) and amplitudecorrection between the I and Q signals, (2) rejection of an image signalby means of complex filtering or a Hilbert transform pair and adder, (3)further bandlimiting, and, (4) translation of the desired signal fromthe near-baseband passband to baseband, which step may include digitalfine-tuning over the near-baseband passband. If the desired signal ispart of a channelized spectrum, the digital fine-tuning capability maybe omitted or reduced to a coarse step-wise digital tuning capabilitywith steps equal to the channel spacing, but a translation fromnear-baseband to baseband is still performed. These steps may beperformed in combination and in various orders to achieve the desiredeffect.

The inventive tuning method provides certain advantages of directconversion receivers, including preferably a single continuous-timedown-conversion stage, lack of image rejection filters with resultingwide possible tuning range, and relatively low frequency at conversionto discrete-time, allowing lower discrete-time processing rates andsimplified decimation filter architecture. The inventive method alsoavoids the problems of 1/f noise and DC offset and self-mixing byavoiding the need for analog amplification of signal frequencies atbaseband or only slightly offset from baseband.

The inventive tuning method further provides certain unique advantages.

For example, some significant advantages result from the inventivemethod's optimal division of tasks between continuous-time anddiscrete-time components.

In the inventive method, continuous-time components perform those tasksfor which they are well suited, particularly the initial downconversionof a high frequency signal, while discrete-time components perform thetasks for which they are well suited, such as signal processing only atbaseband and near baseband frequencies, yielding both relaxedcontinuous-time component tolerances and relatively reduceddiscrete-time processing speed and power requirements.

Further, the size and location of the near-baseband passband utilized inthe invention and of the associated digital fine-tuning range orchannelized spectrum channel spacing, if any, are so organized that thestep size of the coarse-tuned local oscillator may be set to about twicethe digital tuning range without any loss of spectrum coverage. Thedoubled step size relaxes the local oscillator requirements and reducesphase noise generated by the local oscillator. This relaxation of localoscillator (typically a PLL) requirements allows the local oscillator tocover a wider frequency range, so that the invention can take betteradvantage of the wide tuning range afforded by the lack of animage-rejection filter.

In the preferred embodiments, the invention also includes a type IIIHilbert transform, i.e., a case III FIR phase-inverting allpass filter,for image rejection processing. The near-baseband passband utilized inthe invention is then optimally sized and located for use with a typeIII Hilbert transform such that substantial computational and memoryresource savings are realized while maintaining excellent performance.

A fuller appreciation of the above advantages and features and ofadditional advantages and features of the invention will be gained bythose of skill in the art from the detailed description of the preferredembodiments which follows, and from practice of the invention itself.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a diagram of a device according to the present invention.

FIG. 2 is a diagram of the near-baseband passband utilized by presentinvention.

FIGS. 3 and 4 are diagrams illustrating the use of the near-basebandpassband of the present invention with channelized frequency spectra.

FIGS. 5 and 6 are diagrams illustrating the doubled local oscillatorstep size achievable according to the present invention.

FIG. 7 is a diagram showing the preferred size and location of thenear-baseband passband of the present invention in relation to variouscharacteristics of various preferred elements of the present invention.

FIG. 8 is a diagram of presently preferred embodiments of the presentinvention.

FIG. 9 is a diagram showing certain aliasing regions of thenear-baseband passband together with highpass frequency response curvesfor filters for use in the present invention.

FIG. 10 is a diagram showing additional aliasing regions of thenear-baseband passband according to an embodiment of the presentinvention.

FIG. 11 is a diagram of a preferred embodiment of a decimating filterfor use in an embodiment of the present invention.

FIG. 12 is a simulated frequency response curve of the filter of FIG.11.

FIG. 13 is the simulated frequency response curve of FIG. 12 shown on asmaller scale.

FIG. 14 is a simulation plot of quantization noise both with and withoutaliased quantization noise.

FIG. 15 is a diagram illustrating the operation of a Hilbert transformmodified according to the present invention.

FIG. 16 is a diagram illustrating the presently preferred method ofcorrecting phase errors used in the present invention.

FIG. 17 is a diagram illustrating the generation of coefficients for avariable group-delay allpass filter usable in an embodiment of thepresent invention.

FIGS. 18 and 19 are simulated frequency response curves of certainelements of an embodiment of the present invention.

FIG. 20 is a simulated frequency response curve of an-embodiment of thepresent invention.

FIG. 21 is a simulated envelope detector output of an embodiment of thepresent invention.

FIGS. 22 and 23 are simulated frequency response curves of certainelements of an embodiment of the present invention.

FIGS. 24 and 25 are simulated frequency response curves of an embodimentof the present invention.

FIG. 26 is an additional diagram illustrating the use of thenear-baseband passband with channelized frequency spectra.

DETAILED DESCRIPTION OF A PREFERRED EMBODIMENT

A significant aspect of the present invention is the basic division offunctions between discrete-time (digital) and continuous-time (analog)components characteristic of the invention, which is described withreference to FIG. 1.

In FIG. 1, analog portion 12 of a device 10 according to the presentinvention receives an incoming signal from a preferablyremovable/exchangeable antenna 16. A suitable broad-band or tunable RFamplifier 18 then amplifies the signal. Alternatively, the inventioncould also be used to tune an intermediate frequency from previousanalog processing, rather than an incoming signal directly from antenna16 and amplifier 18.

The signal is then split into two signal paths and fed to first andsecond mixers 20, 22. The first and second mixers 20, 22 are suppliedwith a quadrature local oscillator signal from a preferablycoarse-stepped local oscillator 24. The mixing operation translates to anear-baseband passband an upper high frequency spectrum of interest fromabove the frequency F_(LO) of the local oscillator 24 and a lower highfrequency spectrum of interest from below the frequency F_(LO) of thelocal oscillator 24, producing I and Q signals in approximate quadraturerelation.

The near-baseband passband is sufficiently low to provide substantialefficiency gains in the subsequent digital processing, but does notinclude baseband. The near-baseband passband is also sufficiently highto allow a fairly relaxed transition from a cutoff at or near DC to thelower edge of the passband. Problems such as self-mixing products and DCoffsets and 1/f noise are avoided by-high-pass filtering with a relaxedtransition band in filters 26 and 28. Unwanted aliasing is prevented bylow-pass filtering in filters 26 and 28. The I and Q outputs from theanalog portion 16 of the device 10 are then passed to the digitalportion 14 of the device 10.

At least three operations are performed within the digital portion 14 ofthe device 10. First is analog to digital conversion. The I and Qsignals are converted individually into digital signals. Second, phaseerrors (optionally including group delay errors) and amplitude errorsbetween the I and Q channels are corrected, particularly to maximizeimage rejection at and/or near the frequency of the desired signal, andthe channels are combined by a Hilbert transform pair and summing, orfiltering with complex coefficients is employed, in order to reject theundesired mixing image, particularly at the frequency of the desiredsignal. Third, a portion of the now image-rejected signal containing thedesired signal is translated to baseband. The second two operations maybe performed in various orders or to some extent simultaneouslyaccording to the particular design and programming of the digitalportion 14 of the inventive device 10.

The above-described division of functions into analog and digitaldomains, together with the use of the properly located near-basebandpassband, provides important advantages. The number of analog componentsis minimized, and the analog components are employed for those tasks towhich they are most suited: the conversion of high frequencies to lowfrequencies. The digital processing is used only at lower frequencies,allowing lower sampling rates and quantization resolutions to beemployed without substantial loss of signal characteristics, resultingin decreased memory, processing power, and electrical powerrequirements. The near-baseband passband, avoids analog processing ofsignals at or close to DC, thereby avoiding or substantially diminishingproblems associated with 1/f noise and DC offsets and self-mixingproducts. Use of quadrature mixing with subsequent image rejectionavoids the need for relatively high-performance image rejection filtersin the analog portion. Correction in digital processing of phase andamplitude deviations from the desired quadrature relation allowsrelaxation of otherwise relatively strict matching and performancerequirements for the analog filters. Fine-tuning, if employed, ispreferably performed in the digital domain, leaving only coarse-tuningby a coarse-stepped local oscillator to be performed in analogprocessing, thereby reducing the complexity of the local oscillator andthe generation of phase noise.

Another significant aspect of the present invention is preferably thatthe step size S of the local oscillator is twice as large as wouldtypically be permitted, given the range of the digital fine-tuningemployed, or given the channel spacing of the channelized spectrum andthe digital channel tuning employed. This is achieved by properpositioning and sizing of the near-baseband passband and the tuningrange or channelized tuning/translation range of the digital tuningprocess, and takes advantage of the fact that complex I, Q signalscontain twice the spectral information of a real signal.

As illustrated in FIG. 2, the near-baseband passband P may be definedwith reference to a lower frequency F₁ and an upper frequency F₂. Toachieve the preferred effective doubling of the local oscillator stepsize S. F₁ and F₂ are chosen such that F₁ =k·(F₂ -F₁), where k is apositive integer, and S is set to 2·(F₂ -F₁). This insures that thecenter frequency of any desired incoming signal can be translated towithin the positive frequency range of F₁ to F₂ inclusive or thenegative frequency range of -F₁ to -F₂ inclusive by mixing with theappropriate local oscillator frequency. The use of complex I, Q signalsallows the positive frequency range to be distinguished from thenegative frequency range.

For embodiments of the invention designed to tune essentially anydesired frequency from within a given RF range, the digital tuningprocess employed preferably has a range extending from F₁ -F_(H) to F₂+F_(H), where F_(H) is an appropriate hysteresis amount greater than orequal to zero, the effects and usefulness of which will be explainedhereafter. The near-baseband passband P is then defined so as to extendfrom F₁ -F_(A) to F₂ +F_(A) as shown in FIG. 2, where F_(A) is afrequency adjustment equal to at least about W/₂ +F_(H), where W is themaximum bandwidth of the desired signals to be received. This ensuresthat all of the bandwidth of any signal having a center frequencytunable by the digital tuning process will fall within the near-basebandpassband.

A device of the present invention designed to tune essentially anyfrequency can of course be utilized to receive channelized signals. Ifdecreased digital processing is desired in an embodiment designed forchannelized signal reception, the full digital tuning capability overthe entire near-baseband passband can be restricted to discrete digitaltuning in the form of either (1) a translation to baseband from a chosenfrequency within the near-baseband passband (preferably the midpointbetween F₁ and F₂), or (2) a step-wise tuning of selected channelizedfrequencies from the near-baseband passband to baseband. A small amountof fine-tuning may be retained if desired for fine-tuning around thediscrete channelized frequency(ies) within the near-baseband passband.

In embodiments of the present invention employing discrete digitaltuning, the center frequency of each channel of any given channelizedspectrum will be translated to within the frequency range from F₁ to F₂inclusive or from -F₁ to -F₂ inclusive by mixing with one of the variouspossible local oscillator frequencies.

One possibility for selecting F₁ and F₂, with reference to which thenear-baseband passband may be defined, is choosing F₁ and F₂ such thatF₂ -F₁ =N·C where C is the channel spacing and N is the number ofchannels to be contained within the near-baseband passband. F₁ and F₂may be further chosen, along with the local oscillator frequency, suchthat F₁ and F₂ each fall at the midpoint between adjacent channels aftertranslation of the channel frequencies by mixing with the localoscillator signal. This is possible where the permissible localoscillator frequencies are at frequencies one-half of a channel spacingC displaced from integer multiples of the channel spacing, and isillustrated for the case N=1 in FIG. 3.

In FIG. 3, adjacent channels of bandwidth W have been down-converted bymixing with the local oscillator signal. F₁ and F₂ fall between adjacentdown-converted channels. The near-baseband passband P extends from F₁-F_(A) to F₂ +F_(A), where F_(A) is a frequency adjustment equal to1/2(W-C+W_(ft)), where W_(ft) is the width of the digital fine-tuning,if any, provided for fine-tuning around each channel.

FIG. 4 shows the near-baseband passband P in a channelized embodimentusing with N=3, W=C, W_(ft) =0, and F_(H) =0. The local oscillatorfrequency is in this case an integer multiple of the channel spacing.The near-baseband passband P is defined with reference to F₁ and F₂ andthe full-range digital tuning frequency adjustment F_(A), which is equalto (1/2)·(W+W_(ft))·F₂ -F₁ in this case equals (N-1)·C.

The decreased digital processing realized with channelized operation maybe obtained even with irregular intervals between channels or with localoscillator step sizes not evenly divisible by the channel spacing orwith channels not located at integer multiples of the channel spacing. Ageneralized case is illustrated in FIG. 26. For a given channelizedspectrum and a given set of possible local oscillator frequencies, thecenter frequency of every channel is translatable by one of the localoscillator frequencies to within the range F₁ to F₂ inclusive or therange -F₁ to -F₂ inclusive. The channel having a center frequency aftersuch translation the absolute value of which is closest to (but notgreater than) F₂ is used to determine the upper edge of thenear-baseband passband P. The center frequency of such channel aftertranslation may be either negative or positive, but is illustrated inFIG. 26 as positive channel C₂. The upper edge of the near-basebandpassband P (the edge with the greatest absolute value) is then locatedat the edge of the bandwidth of channel C₂ furthest from DC, plusanother W_(ft) /2 from DC, which is half the width of any digital finetuning range. Similarly, the channel having a center frequency aftertranslation the absolute value of which is closest to (but not lessthan) F₁ is used to determine the lower edge of the passband. The centerfrequency of such channel after translation may be either negative orpositive, but is illustrated in FIG. 26 as negative channel C₁. Thelower edge of the near-baseband passband P (the edge with the leastabsolute value) is then located at the edge of the bandwidth of channelC₁ closest to DC, plus another W_(ft) /2 toward DC. The resultingfrequency adjustments F_(A1) and F_(A2) are shown in FIG. 26.

Note that in the above examples and throughout the specification andclaims, it should be understood that the near-baseband passband refersto that portion of the frequency spectrum to which signals of interestare to be translated in continuous time for further processing indiscrete time. The actual physical passband created by the frequencyresponse of the filters 26 and 28 of FIG. 1 may, of course, be largerthan the near-baseband passband itself, and indeed it is preferred thatthe actual passband be somewhat larger, so that the corners of filters26 and 28 do not appear within the near-baseband passband. Preventingthe corners from appearing in the near-baseband passband reduces groupdelay variation that can cause degradation in image rejection and canworsen intersymbol interference.

Whether in an embodiment with essentially continuous digital fine-tuningor with channelized digital tuning, the frequencies F₁ and F₂ areselected such that F₁ =k·(F₂ -F₁), where k is a positive integer. Mostpreferred is k=1 as in FIG. 2, but other values can be used, such as k=2as shown in FIG. 4. The effective doubling of the permissible step sizeS of the local oscillator results in part from utilization of thisequation as illustrated below with respect to FIGS. 5 and 6.

For a given local oscillator frequency F_(LO), both an upper highfrequency spectrum of interest and a lower high frequency spectrum ofinterest are translated to the near-baseband passband. By means ofimage-rejection processing employed in the digital domain, either thenear-baseband image of the upper high frequency spectrum of interest orthe near-baseband image of the lower high frequency spectrum of interestmay be rejected, allowing selection of either the upper high frequencyspectrum of interest or the lower high frequency spectrum of interestfor further processing. Because of the positioning and size of thenear-baseband passband and associated digital tuning, whether continuousfine-tuning or stepwise tuning, alternate selection of the upper andlower high frequency spectra of interest can be used to providenon-redundant coverage of the broadband frequency spectrum from whichthe desired signal is to be received. Any desired frequency may then betranslated to the near-baseband passband with the local oscillator stepsize S set to twice the digital tuning range, i.e., S set equal to 2·(F₂-F₁).

FIG. 5 shows a portion of the positive frequency spectrum graphed on alinear scale. Each possible value of F_(LO) is indicated with an arrowand labeled with a letter or letters and a backslash. The letters arealso used to label a number of frequency regions with a channelizedsignal in each. This represents an embodiment for a channelized spectrumwith a near-baseband passband sized to fit one channel, as in FIG. 3.The letters labeling each possible value of F_(LO) correspond to theletters labeling the regions translated to the near-baseband passband bythat value of F_(LO). If F_(LO) is at A\D, for example, regions A and Dare translated to the near-baseband passband. The letter to the left ofthe backslash corresponds to the letter labeling the lower highfrequency spectrum of interest for a given F_(LO), while the letter tothe right corresponds to the letter labeling the upper high frequencyspectrum of interest for that given F_(LO).

To translate to the near base-band passband the channelized signalfrequency within region F, for example, the local oscillator frequencyF_(LO) would be set to the C\F position. The desired signal frequencywould then fall within the upper high frequency spectrum of interest ofthe local oscillator frequency. The image of region C, the lower highfrequency spectrum of interest, would be rejected by the digital imagerejection processing, leaving F as the selected region.

Similarly, to tune the channelized signal frequency within region Gshown in FIG. 5, the local oscillator frequency F_(LO) would be set tothe G\J position. The desired signal frequency would then fall withinthe lower high frequency spectrum of interest of the local oscillatorfrequency, and the image of region J would be rejected by the digitalimage rejection processing, leaving G selected.

While k=1 is preferred as noted above, other values are possible such ask=2, illustrated in FIG. 6 for an embodiment with essentially continuousdigital fine-tuning. The upper and lower high frequency spectra ofinterest are now each about two tuning ranges separated from theapplicable local oscillator frequency F_(LO), but the same completecoverage, with a step size S=2·(F₂ -F₁), is provided. To tune a signalfrequency within region C, for example, the local oscillator frequencywould be set to the C\H position, and the lower high frequency spectrumof interest would be selected.

The proper F_(LO) to receive a given desired signal frequency F_(t) maybe found by any appropriate method. For example, the proper F_(LO) maybe found generally by setting NLO=floor(F_(t) /S+1/2), which is thefactor NLO such that NLO·S is the nearest F_(LO) to the desired signalfrequency F_(t). If NLO·S≧F_(t), the proper F_(LO) to employ totranslate F_(t) to the near-baseband passband is then given generally by(NLO+(-1)^(k) ·floor(k/2+1/2))·S, with F_(t) found in the upper highfrequency spectrum of interest if (-1)^(k) <0, and in the lower highfrequency spectrum of interest otherwise. Similarly, if NLO·S≦F_(t), theproper F_(LO) is given by (NLO-(-1)^(k) ·floor(k/2+1/2))·S, with F_(t)in the upper high frequency spectrum of interest if (-1)^(k) >0, and inthe lower high frequency spectrum of interest otherwise. (The ambiguityin F_(LO) selection at NLO·S=F_(t) is caused by the overlap of adjacenthigh frequency spectra of interest as seen in FIG. 6, which allows adesired signal of frequency F_(t) equal to NLO·S to be translated to thenear-baseband passband by either of two possible values of F_(LO).)

To avoid having to repeatedly change the value of NLO when fine-tuningaround a signal frequency F_(t) about equal to NLO·S, the hysteresisamount F_(H) for essentially continuous fine-tuning embodiments may beset to a value greater than zero. This allows fine tuning on both sidesof a signal frequency F_(t) equal to about NLO·S with only one localoscillator frequency F_(LO), and widens each high frequency spectrum ofinterest by 2·F_(H). If a desired frequency F_(t) moves out of a firstwidened high frequency spectrum of interest associated with a firstF_(LO), a second F_(LO) is selected. If F_(t) then moves back into thefirst widened high frequency spectrum of interest, the second F_(LO) ismaintained until F_(t) is within the first widened high frequencyspectrum of interest by the distance F_(H). Thus excessive switchingfrom one F_(LO) to another is prevented.

If the invention is used to tune an intermediate frequency from previousanalog processing, either a local oscillator in the previous analogprocessing or the quadrature local oscillator 24 may be varied and theother local oscillator set to a fixed frequency. The effective doublingof the permissible step size S of the varied local oscillator ispreferably retained in either case through the alternate selection ofthe upper and lower high-frequency spectra of interest.

While the actual frequencies F₁ and F₂, selected as described above,will vary with the particular application, it is currently preferredthat F₁ be at least about W and that, in general, F₂ be not more thanabout 150 kHz. In some applications, however, F₂ may be many times thisgeneralized upper limit. It is currently preferred that F₂ -F₁ be atleast about 20 kHz. In embodiments with full-range digital tuning, it iscurrently preferred that F₂ -F₁ be within the range of about 3·W toabout 5·W.

Another significant aspect of the present invention is the preferred useof a type-III Hilbert transform in the image rejection processing in thedigital domain. A type III Hilbert transform enjoys nearly a 2:1efficiency advantage over a similar standard type IV Hilbert transform,because every other impulse response sample is zero. The performanceenvelope of the type III Hilbert transform is symmetrical and centeredon f_(s) /4 (where f_(s) is the sampling frequency employed), fallingoff symmetrically approaching DC and f_(s) /2. While the performance ofthe type III falls off relative to the type IV as frequencies approachthe Nyquist frequency of f_(s) /2, the present invention avoids anydisadvantage from this characteristic as will be seen below with respectto FIG. 7.

Due to the preferred spacing from DC of the near-baseband passband ofthe present invention as illustrated for example in FIG. 2, thenear-baseband passband is sufficiently separated from DC for anefficient and accurate Hilbert transform to be performed. The relativelywide transition band to DC also affords relaxed filter specifications.To take advantage of the type III transform's efficiency and to provideeven more relaxed filter specifications, the present inventionpreferably employs a type III Hilbert transform with a sampling rate Rentering the Hilbert transform equal to 2·(F₁ +F₂). This is equivalentto centering the near-baseband passband at R/4. Some of the advantagesof this arrangement are illustrated for the case k=1 in FIG. 7.

FIG. 7 shows the near-baseband passband P of the present inventionlocated to encompass a digital tuning range between F₁ and F₂ with F₁=k·(F₂ -F₁) with k being a positive integer, in this case 1. The stepsize S of the analog local oscillator is also shown for reference. Theuse of a type III Hilbert transform with an entering sampling frequencyR=2·(F₁ +F₂) results in the illustrated performance curve H for thepreferred type III Hilbert transform. The performance curve H issymmetrical with the best performance at the location of thenear-baseband passband P, with symmetrically reduced performance towardDC and the Nyquist frequency of R/2.

The near-baseband passband is also situated so as to substantially avoid1/f noise represented by the N_(1/f) spectrum shown, and quantizationnoise Q from a presently most preferred delta-sigma analog to digitalconversion. The transition bands T are also sufficiently broad to relaxfiltering requirements in both the analog and digital domains as will beshown in greater detail below.

A pair of preferred embodiments of the device of the present inventionimplementing the methods and having the characteristics and advantagesdiscussed above are shown in greater detail in FIG. 8. The device 10shown in FIG. 8 corresponds to the device 10 shown in FIG. 1, but withdetails of presently preferred embodiments shown in the digital portion14 of FIG. 8. Accordingly, analog portion 12 shown in FIG. 8 is asdescribed above with reference to FIG. 1.

The analog I and Q signals are received into digital portion 14 from theanalog portion 12 of the device 10 and are converted into digitalsignals by delta-sigma modulators 30, 32 most preferably third-orderdelta-sigma modulators, with one-bit wide output. The delta-sigmamodulators sample the I and Q signals at an over-sampling rate R₀.Decimation filters 34 and 36 filter the output of the delta-sigmamodulators so as to substantially reject frequencies which would aliasinto the near-baseband passband on decimation, and decimate the signal,such that the output sample rate is equal to R, the desired inputsampling frequency at a Hilbert transform pair, comprised of a Hilberttransform 38 and allpass filter 40, which follows.

An alternate embodiment, shown in FIG. 8 by the dashed-line alternatesignal paths I_(A) and Q_(A), does not employ oversampling. Instead, theI and Q signals are sampled by analog to digital converters 42 and 44 atthe rate R, the input sampling frequency at the Hilbert is transformpair 38 and 40, and converted into digital signals preferably 12 to 16bits wide, depending on the dynamic range requirements of theapplication. Thus no decimation is required between analog to digitalconverters 42 and 44 and Hilbert transform pair 38, 40. For thisalternate embodiment, the near-baseband passband of the presentinvention provides somewhat relaxed anti-aliasing lowpass filterspecifications, as illustrated in FIG. 9.

The near-baseband passband P of the present invention, for the case k=1,is shown in FIG. 9. P ends at (k+1)·S/2+F_(A). The region AR_(R) is thefirst (lowest frequency) region to alias into P at a sampling rate of R.AR_(R) begins at R-(k+1)·S/2-F_(A). Accordingly, the passband of theanti-aliasing filter represented by response curve 46 must extend atleast to (k+1)·S/2+F_(A), while the stop band must begin at or beforeR-(k+1)·S/2-F_(A). This prevents aliasing into P while allowing a fairlyrelaxed transition band between the passband and stop band. A highpassfilter would preferably be employed with a passband beginning at thelower edge of P, which is given by k·S/2-F_(A). These two filterstogether then comprise filter 26, for example, in FIG. 8. The lowpassfilter can be an eighth order switched-capacitor elliptical lowpassfilter, for example. The passband of the filter 26 preferably extendseven beyond the edges of P such that the corners of the filter, withtheir typically large group delay, are not within P.

The relatively high order low-pass filters typically needed formoderately relaxed transition bands such as the transition band inresponse curve 46 of FIG. 9 can cause less efficient image rejection dueto small variations in pole and zero locations between the filters 26and 28 in the device 10 of FIG. 8. In the most preferred embodimentshown in FIG. 8 by the I and Q solid line signal paths, oversamplingallows use of much lower order anti-aliasing filters, with correspondingimprovements in image rejection.

The relaxed anti-aliasing filter transition band obtainable withoversampling is illustrated in FIG. 9, where R₀ is the oversamplingsampling rate, with R₀ =M·R where M is the rate of oversampling. M=3 isshown for illustration purposes in FIG. 9. AR_(Ro) is then the firstaliasing region, i.e., the lowest frequency region to alias into P at asampling rate of R₀. AR_(Ro) begins at R₀ -(k+1)S/2-F_(A). Accordingly,the stopband of the anti-aliasing filter represented by response curve48 must begin at or before R₀ -(k+1)·S/2-F_(A), with the same passbandregion as response curve 46. Response curve 48, together withoversampling, thus prevents aliasing into P while allowing a veryrelaxed transition band between the passband and stop band of theanti-aliasing filter. In practice, even greater oversampling rates than3 are desirable, with M=32 currently most preferred. A 2-pole Chebychevtype I low pass filter is then preferred for the low pass filter portionof filters 26 and 28.

Note that, as discussed with reference to FIG. 26, the frequencyadjustment F_(A) may have differing values at the upper and lower edgesof the near-baseband passband P.

In the most preferred embodiment, decimating filters 34 and 36 followthe delta-sigma modulators 30 and 32, respectively. One of thedecimating filters 34 and 36 preferably includes a group delaycorrection. The output of the delta-sigma modulators 30 and 32 ispreferably one bit wide, allowing group delay correction to beimplemented with a variable shift register in the signal path. One-bitsignal width, together with the near-baseband passband and otherfeatures of the present invention, also makes practical an efficientsingle stage implementation of filters 34 and 36 with no multiplicationrequired.

The aliasing regions of concern in the design of filters 34 and 36 areillustrated for example in FIG. 10. The output of filters 34 and 36 isto be sampled at a rate R which is equal to R₀ /M, where R₀ is theover-sampling sampling rate. M=3 is used in FIG. 10 for illustrationpurposes. The first aliasing region AR_(R) is the first, i.e. lowestfrequency, region to alias into P due to the sampling at rate R.Subsequent aliasing regions AR are also shown in FIG. 10 to the right ofAR_(R). The desired decimating filter should thus have a passband at Pand stopbands of at least the same width as P at each aliasing region.All other frequency regions may be left unconstrained in the filterdesign process. Leaving regions which do not alias into thenear-baseband passband P unconstrained, particularly with the size andposition of P relative to R as preferred in the present invention,allows significant reduction in filter order and/or length such that asingle stage decimation filter with good performance and reasonably lowprocessing and memory requirements can be implemented.

A preferred design for a single stage decimation filter for use asfilter 34 and/or 36 is shown in FIG. 11. The filter includes: 32-bitregisters 50a-50i, operators 52a-52d, look-up tables 54a-54d with alook-up table address generator 56, a 22-bit accumulator 58, and atruncator 60 and a decimator 62.

The 32-bit register 50a receives signal bits from the associatedupstream one-bit delta-sigma modulator until the register 50a is full.Each time register 50a is full, the contents of each of the 32-bitregisters 50a-50h are shifted into the 32-bit registers 50b-50irespectively. Because of the one-bit signal width and the symmetricalfilter coefficients and folded-over filter architecture, the operators52a-d can be used to efficiently determine the filter output withoutmultiplication.

In the operators 52a-d, each of the 32 signal bits from one associatedregister is exclusive or-ed with the signal bit at the same distancefrom the center of the filter's delay line from the other respectivelyassociated register. If the bits are not equal, a zero is added to thecontents of the accumulator 58. If the bits are equal and positive,twice the value of the applicable coefficient is added to the contentsof the accumulator 58, and if the bits are equal and negative, negativetwice the value of the applicable coefficient is added to the contentsof the accumulator 58. This can be easily implemented by storing not theactual filter coefficient values in the look-up tables 54a-54d, buttwice the actual coefficient values. Then if two signal bits compared inthe operator 52a for example are equal, the sign of one can be used asthe sign bit to be sent to the accumulator 58 along with the doubledcoefficient value from the look-up table 54a.

Each of operators 52a-52d operates in parallel on two of the 32-bitregisters 50b-50i, and sends its output to accumulator 58 in parallel.Once all coefficients have been summed in accumulator 58, truncator 60takes only the 16 most significant bits from accumulator 58. Decimator62 represents the decimation performed in the operation of this filter.

Table I below contains Matlab® code for generating filter coefficientsfor the filter illustrated in FIG. 11 for use with the near-basebandpassband of the present invention with k=1 and the near-basebandpassband centered at 1/4 of the Nyquist frequency. (Matlab® is softwarefor digital signal processing analysis and development available fromThe MathWorks, Inc., Natick, Mass., U.S.A.) In the code in Table I, thevariable fs is the sampling frequency entering the Hilbert transform andis set to 128 kHz. N is the filter order, which is set to 255, resultingin 256 FIR filter taps, which number is desirable as a power of 2 givingeasier implementation in a DSP, and because it provides sufficient tapsto significantly reduce noise at each alias of the near-basebandpassband. R is the weight of the stopband constraint versus passbandconstraint, and is set to 100, resulting in very high stopband rejectionat the expense of some passband ripple. Mds is the over-sampling anddecimation ratio, and is set to 32.

Table II below gives an example of doubled filter coefficient values foruse in the look-up tables 54a-54d. Note that look-up tables 54a and 54brequire 32×13 bits of storage, while look-up table 54c needs 32×14, andlook-up table 54d needs 32×16.

The resulting simulated frequency response of the filter in FIG. 11 isshown in FIGS. 12 and 13. In FIG. 12, the filter response at thenear-baseband passband, located at 21.33-42.67 kHz in this example, maybe seen. In FIG. 13 with a smaller scale, the repeating stopbands ataliasing regions of the near-baseband passband may be seen, includingstopbands at about 80-100 kHz, 140-160 kHz, etc.

One important criteria for judging the performance of the filter of FIG.11 is the reduction of quantization noise from the delta-sigmamodulator, particularly from higher aliasing regions which would aliasinto the near-baseband passband. FIG. 14 shows the noise due toquantization after filtering and decimation without (lower trace) andwith (upper trace) the aliased quantization noise. Noise floors in thenear-baseband passband located in this case at 21.33-42.67 kHz are stillat quits acceptable levels, even with the addition of the aliased noise.

The preferred design of the Hilbert transform 38 of the device 10 inFIG. 8 is of course type III, but with at least one modification. TypeIII Hilbert transforms have an odd number of taps, with the center tap,and taps displaced an even number of taps from the center tap, set tozero. The Hilbert transform 38 is modified by having a variable non-zerocoefficient present at the center tap, i.e., at the sample of itsimpulse response the index of which corresponds to half the length ofthe transform delay line. This modification enables the Hilberttransform 38 to function as if in parallel with an all pass filter withvariable gain, as shown schematically in FIG. 15. As the contributionfrom the allpass portion increases or decreases from zero, the phasechange caused by the Hilbert transform is varied up or down from 90degrees, allowing efficient correction of phase errors. The othercoefficients of the Hilbert Transform may also be varied along with thecentral coefficient to implement correction of amplitude errors betweenthe I and Q channels. Variable gain for amplitude error correction mayalso be implemented in the allpass filter 40 if desired.

In implementing any type of error correction between the I and Qchannels; the errors should be corrected not to maximize coherence ofthe desired signal but to maximize rejection of unwanted mixing imagesat and near the frequency of the desired signal. This is illustrated forphase error correction in FIG. 16. An undesired Q phasor UQP is alreadydisplaced by amount "a" toward an exact opposite phase relation with theI phasors IP. The Hilbert transform is accordingly employed to rotatethe undesired Q phasor UQP and the desired Q phasor DQP by a phasecorrection amount PC such that PC=90°-a. This rotation moves UQP intodirect phase opposition to the I phasors IP, while DQP is not completelyphase corrected, being out of phase by amount "a" plus amount "b."

All error correction between the I and Q channels is preferablyimplemented by running a characterization of each device upon completionof device fabrication, and then storing desired correction factors in amemory associated with the digital portion of the device. Othertechniques such as techniques to continuously detect and correct sucherrors may also be employed, if desired. Temperature sensing capabilitymay also be provided if desired, such that correction factors may bedependent on temperature for optimized image rejection under variousclimatic conditions.

Allpass filter 40 is designed with nominal group delay equal to thegroup delay of Hilbert transform 38. The Hilbert transform 38 or theallpass filter 40 is also enabled to change the sign of its output, inorder to switch from rejecting the image of the upper high frequencyspectrum of interest to rejecting the image of the lower high frequencyspectrum of interest, and vice versa. As explained above, thisswitching, combined with the correct step size S of the local oscillator24 and with an appropriately sized and located digital tuning rangeand/or near-baseband passband, results in twice the local oscillatorstep size S that would otherwise be possible for a given tuning range ora given channel spacing of a channelized spectrum.

Particularly for the embodiment of the device 10 in FIG. 8 employing thealternate signal paths I_(a) and Q_(a), group delay correction may alsobe performed in the Hilbert transform pair, if desired, by providing theallpass filter 40 with variable coefficients corresponding to variablyoffset samples of the sinc function. (The sinc function is defined as:)##EQU1## For zero time shift, the coefficients are given by samples ofthe sinc function at zero+nπ with n an integer, which results in valuesof zero everywhere except at n=0, where the sinc function returns avalue of 1. Coefficients for a time offset equal to 1/4 of one sample atany given sampling frequency may be generated by sampling the sincfunction at nπ/4, the central 7 samples of which are shown in FIG. 17.These seven samples give seven coefficient values, with nπ/4 moreobtainable as desired by extending the sinc function sampling further inboth directions. An appropriate window (such as Hamming, Blackman, orKaiser) should, of course, be applied to the coefficient values.

Table III below contains Matlab® code for generating the coefficientsfor the modified Hilbert transform 38 of FIG. 8. In the code, fs is thevariable for the sampling frequency entering the Hilbert transform andis set to 128 kHz. The fbw variable represents the bandwidth of thesignal of interest, in this case set to 6400 for an 8000 bps QPSKsquare-root raised-cosine digital signal with an excess bandwidthsetting (Beta) of 0.6. The fref variable is a reference frequency of thelocal oscillator equal to the local oscillator step size which is inthis case 42.67 kHz. The fref variable is used in this code to definethe passband of the transform according the preferred embodiment. Nh isthe filter order, set to 16, resulting in 17 filter taps. (Note thatthis code applies the transform to the Q channel rather than the Ichannel--either is fine, as long as the other channel has a 0° allpass.)

After the Hilbert transform pair 38, 40 of the device 10 of FIG. 8, thesignals from the I and Q channels are combined by adder 64 resulting ina real, image-rejected near-baseband signal. This signal is fed to avariable band-pass decimating filter 66.

The variable band-pass decimating filter 66 is designed by firstdesigning a prototype filter to have a passband of width W straddlingDC, where W is the bandwidth of the desired signal. Similarly to thepreferred embodiment of decimating filters 34 and 36, stopbands also ofwidth W are defined for the prototype filter only at locations aliasedto the passband by the decimation sampling rate R_(D). Transition bandsmay again be left unconstrained during filter design. To provideadequate transition band width while preventing undesired aliasing,R_(D) must be somewhat greater than W.

Once the prototype filter coefficients are obtained, the position of thepassband and the stop bands are varied as desired by multiplication ofthe filter coefficients by a complex exponent to select from thenear-baseband passband a desired signal spectrum of width W. Thealiasing caused by the decimation then translates the selected spectrumto within R_(D) /2 of baseband. The variable band-pass decimating filterthus performs a tuning function with a resolution of R_(D) /2.

Matlab® code for determining the coefficients of a filter useable as thevariable bandpass decimating filter 66 is presented below in tables IVand V. The code in table IV determines the coefficients for a prototypefilter with a passband at DC of width W and seven stopbands of width Wat intervals of R_(D) to either side of DC. In the code in table IV, Nis the filter order and is set to 63, resrulting in 64 FIR filter taps,providing adequate interference attenuation with a power of 2 lengthwhich is typically more easily implemented in a DSP. R is the relativeemphasis on stopband performance relative to passband performance and isset to 50, resulting in good stopband rejection with reasonable levelsof passband ripple. Variable f1 represents the sampling frequency at theHilbert transform pair and is set to 128 kHz. Variable f2 represents theoutput sampling frequency of filter 66 and is set to 16 kHz, giving adecimation ratio of M=8. Variable fbw represents the bandwidth of thesignal of interest, in this case a 8000 bps QPSK square-rootraised-cosine digital signal with an excess bandwidth setting (Beta) of0.6.

The code in table V adjusts the coefficients generated in the code intable IV, which are contained in variable b. Variable fs is the samplingfrequency at the Hilbert transform pair, set to 128 kHz here. Variablefshift is the frequency to which the passband of the filter 66 is to beshifted.

Final fine-tuning is performed after filter 66 by fine-shifting bymixing with a complex exponential is signal. This fine shifting bringsthe desired signal to baseband from the location within R_(D) /2 ofbaseband to which it was aliased by filter 66. The complex exponentialsignal is supplied by a digital quadrature local oscillator 68 and mixedwith the complex signals by digital mixer 70. The complex signals arethen filtered and decimated at a decimation rate of M=2 by filters 72,74 matched to the pulse of the desired signal, which filters rejectfrequencies in the transition bands of the variable bandpass decimatingfilter and in regions aliasing into the desired signal. Significantsuppression of transition bands is thus effectively postponed until thesignal reaches filters 72, 74, at which point the sampling frequency hasbeen reduced to R_(D) =R/8, and the spectrum of interest has beenreduced to within R_(D) /2 of baseband, allowing for relativelyefficient sharp-cutoff filtering. The resulting signals are thendemodulated by a quadrature demodulator. For other types of signals,other typical demodulation procedures and devices may be used after thefine-shifting operation.

Simulated frequency response curves for the embodiment of the device 10of FIG. 8 not employing oversampling are seen in FIGS. 18-20.

FIG. 18 shows the continuous-time filtering frequency response curve CTtogether with the Hilbert transform frequency response curve HT. The CTcurve shows the desired attenuation of frequencies near DC, togetherwith anti-aliasing low pass filtering with a transition band from about2.25 to about 3. Beginning the transition band above 2, the upperboundary of the near-baseband passband in this embodiment, avoidsincluding the corner of the lowpass filter within the near-basebandpassband, thereby avoiding significant group delay variations which canincrease intersymbol interference. The beginning of the stopband at 3could actually be relaxed, allowing the stopband to begin as late as 4(minus F_(A)) without resulting in aliasing into the near-basebandpassband at 1 to 2, given a sampling frequency of R=6 as preferred witha 1 to 2 near-baseband passband. The HT curve shows rejection of themixing image at -1 to -2 on the x axis.

FIG. 19 shows a variable passband decimating filter frequency responsecurve VDF and a matched filter frequency response curve MF. The VDFcurve shows a passband centered at 1 with seven stopbands to either sideat intervals of 0.75=R/8=R_(D). The matched filter frequency responsecurve MF is shown aligned with the VDF curve to reject signals withinthe transition band of the VDF curve. Translation to baseband is notshown.

FIG. 20 shows the system frequency response resulting from the cascadeof the frequency responses shown in FIGS. 18 and 19.

FIG. 21 shows an envelope detector output resulting from simulatedenvelope detection of the simulated output of the device 10 of FIG. 8.Intersymbol interference is -28.55 dB, well below the maximum allowablein most digital modulation schemes.

FIGS. 22-25 show simulated frequency response curves for the embodimentof the device 10 of FIG. 8 employing oversampling, but with M=16 (16times oversampling) for illustration purposes rather than M=32 ascurrently most preferred.

FIG. 22 shows the continuous-time filtering response curve CT, with thevery relaxed upper transition bands employable with oversampling. Thefrequency curve HT response of the Hilbert transform and the frequencyresponse curve DF of the decimating filters 34, 36 are also shown. TheDF curve shows the desired passband at about 1 to 2 on the x axis withstopbands of the same width repeating at intervals of 3 on either side.

FIG. 23 shows the curves of FIG. 22 on a smaller scale. Theunconstrained transition bands of the DF curve may be seen, as well asthe image rejection of the HT curve at 1 to 2.

FIGS. 24 and 25 show a simulated system frequency response resultingfrom the embodiment of device 10 in FIG. 8 using oversampling at M=16.Attenuation of unwanted signals and noise in this simulated embodimentmeets the requirements of most commercially available mobile radioequipment (about 75 dB).

While the above described preferred embodiments are only the presentlymost preferred embodiments, certain additional general advantages of thepresent invention may be seen therein.

The particular division of functions between analog and digital portionsof the device 10 allows sufficiently relaxed requirements for both theanalog and digital portions that each can be implemented individually ona single integrated circuit. The processing power and memoryrequirements of the embodiment not employing oversampling are low enoughto allow implementation of the entire digital portion in a currentgeneral purpose DSP. Even the oversampling embodiment may potentially beimplemented in next-generation general purpose DSPS, or in an ASIC withno more complexity or power requirements than a general purpose DSP, orin a current DSP with a discrete component or two for performing thedelta-sigma modulation. Single chip implementation of the entire deviceis even possible with adequate shielding of the analog portions fromdigital portion noise.

While not required, all of the filters in the digital domain may beimplemented as single stage filters due in part to the location of thenear-baseband passband of the present invention, and to the use ofnon-constrained transition bands. Single stage filtering is advantageousin the variable bandpass decimating filter 66, since only a single stageof coefficients must be varied to alter the passband location. Thepassband could thus be varied in real time to follow variations in aparticular signal of interest. Single stage filtering is also veryadvantageous in the oversampling decimating filters 34, 36 because itallows elimination of multipliers and implementation with adders only.

The preferred use of a modified type III Hilbert transform allowsparticularly easy and efficient correction of phase errors between thequadrature I and Q signals. The use of a one bit wide signal path in theoversampling embodiment also allows easy correction of group delaydifferences between the I and Q signals.

As known to those of skill in the art, modulation and transmission of RFsignals may be performed essentially by reversing the demodulationprocess. The device of the present invention may accordingly be adaptedby those of skill in the art for use as a transmitter/receiver, ifdesired. In this case, the signal flow shown in FIGS. 8 would bereversed. I and Q signals from a baseband modulator would be sentthrough transmit stages analogous to the receive stages shown. Forexample, a splitter would be substituted for the adder, interpolatingfilters substituted for the decimating filters, and digital to analogconverters substituted for the analog to digital converters. The Hilberttransform pair and local oscillator(s) would function for transmissionin the same manner as they function for reception. This substitution ofanalogous transmit stages for receive stages should be readily apparentto those of skill in the art.

Having illustrated and described the principles of the invention in apreferred embodiment, it should be apparent to those skilled in the artthat the embodiment can be modified in arrangement and detail withoutdeparting from such principles. In view of the many possible embodimentsto which the principles of the invention may be applied, it should berecognized that the illustrated embodiment is only a preferred exampleof the invention and should not be taken as a limitation on the scope ofthe invention. Rather, the invention is defined by the following claims.I therefore claim as my invention all such embodiments that come withinthe scope and spirit of the following claims.

                  TABLE I    ______________________________________    %       Define the delta-sigma oversampling frequency    %       from the oversampling ratio    %       and the discrete-time system sampling frequency    %       (input to the Hilbert transform pair)            fds = fs * Mds;    %       Define weight of passband as 1/R and weight of all    %       stopbands as 1            wt =  1/R ones(1,floor(Mds)- 1!;    %       Define passband of filter            f =  fs/6 fs/3 !;            m =  1 1 !;    %       Define stopbands of filter only at frequency regions    %       which would alias into passband    for k = 1:ceil(Mds)- 1,            % Stopbands fs/2 apart because real filter            f(2*k+1:2*k+2) =   -fs/12 fs/12! + . . .            (fs/2*k+fs/4) *ones(1,2);            m(2*k+1:2*k+2) =   0 0 !;    end    %       Adjust for 1 = Nyquist freq.            f = f ./ (0.5*fds);    %       Compute filter using Remez exchange algorithm            bds = remez(Nds,f,m,wt);    ______________________________________

                  TABLE II    ______________________________________    LOOK-UP TABLE COEFFICIENTS    54a     54b            54c     54d    ______________________________________    164     4454           -6504   7308    222     4538           -7064   9174    276     4602           -7626   11106    348     4646           -8146   13098    426     4668           -8638   15138    514     4664           -9092   17224    608     4636           -9508   19342    710     4582           -9876   21486    820     4498           -10194  23648    936     4384           -10456  25816    1060    4238           -10656  27980    1190    4060           -10790  30134    1328    3850           -10852  32264    1472    3604           -10838  34362    1622    3324           -10742  36418    1778    3008           -10562  38420    1940    2658           -10292  40360    2106    2272           -9930   42228    2276    1852           -9474   44016    2450    1398           -8920   45712    2624    912            -8266   47310    2802    394            -7510   48798    2978    -156           -6652   50172    3154    -732           -5692   51424    3328    -1334          -4630   52546    3498    -1960          -3468   53532    3664    -2604          -2204   54378    3822    -3266          -844    55076    3972    -3940          612     55630    4112    -4624          2160    56028    4240    -5304          3794    56288    4354    -5996          5512    56372    ______________________________________

                  TABLE III    ______________________________________    %        Define the zero degree delay as a unit sample in    %        the center of an FIR filter of equal length to the    %        90 degree Hilbert transform filter. Only the    %        samples before the unit sample need to be    %        implemented in practice.             bhI =  zeros(1, (Nh-1)/2) 1 zeros(1, (Nh-1)/2)!;    %        Define passband of the Hilbert transform             fhilb =  (fref/2 - fbw/2) (fref + fbw/2)! / (fs/2);    %        Define the 90 degree Hilbert transform using Remez    %        exchange algorithm             bhQ = remez(Nh,fhilb,  1 1!, `Hilbert`);    %        Scale amplitude of Q channel coefficients for gain    %        imbalance compensation             bhQv = QG .* bhQ .* SB;    %        Adjust amplitude of center Q channel coefficient to    %        vary phase from 90 degrees. This provides phase    %        imbalance compensation.             bhQv((Nh/2)+1) = tan((2*pi)/360 * QP);    ______________________________________

                  TABLE IV    ______________________________________    function b = dbf(N,R,f1,f2,fbw)    %      b = dbf(N,R,f1,f2,fbw)    %      Decimating Bandpass Filter    %      Nth-order bandpass FIR with decimation and    %      asymmetrical frequency response    %      R parameter (50 suggested) determines relative    %      importance of passband and stopbands    %      f1 is input sampling rate    %      f2 is output sampling rate    %      fbw is 2-sided bandwidth of interest    %      Calculate cutoff frequency of prototype LPF (1/2 BW    %      of interest)           fc = fbw/2;    %      Iterate to get all stopband regions except at f=1           M = f1/f2;    %      Parks McClellan: define bands    %      Define passband of filter           f =   0 fc ! ;           m =   1 1  ! ;    %      Define weight of stopband vs. passband based on R           parameter    %      50 gives Rp<0.01dB with Rs<-100dB    %      Define weight of passband as 1/R and weight of all    %      stopbands as 1           wt =   1/R ones(1,floor(M/2))!;    %      Define stopbands of filter only at frequency regions    %      which would alias into passband           for k = 1:ceil(M/2)-1,            f(2*k+1:2*k+2) =   -fc fc ! + f2*k*ones(1,2);            m(2*k+1:2*k+2) =   0 0 !;    end    %      If M is even, append a fixed stopband at Nyquist    %      frequency    if ceil(M/2)==M/2            f(M+1:M+2) =   f1/2-fc f1/2 !;            m(M+1:M+2) =   0  0  !;    end    %      Adjust for 1 = Nyquist freq.           f = f ./ (0.5*f1);    %      Compute filter using Remez exchange algorithm           if N>=3            b = remez(N,f,m,wt);           else            %Order less than 3 is defined to be just a            %zero-order            %allpass            b = 1    end    %      Define transfer function denominator coefficients as    %      simply a one followed by zeroes           a =  1 zeros(1,max(size(b))-1))!;    %      Make sure H(0)=1           k = freqz(b,a,linspace(0,pi));           b = b ./ max(abs(k));    %end of function    end    ______________________________________

                  TABLE V    ______________________________________    n = l:length(b);    b = b . * exp(i*2*pi(fshift/fs)*n));    ______________________________________

I claim:
 1. A device for effecting frequency translation and selectionof a signal of interest, said device comprising:a. an analog portionincludingi. a local oscillator for providing a first local oscillatorsignal having a frequency F_(LO) and a second local oscillator signalhaving the frequency F_(LO) approximately in quadrature to the firstlocal oscillator signal, ii. a first mixer for mixing the first localoscillator signal with an incoming signal providing thereby a firstmixer output comprised of an upper high frequency signal spectrum ofinterest above F_(LO) and a lower high frequency spectrum of interest below F_(LO) both translated to a near-baseband passband by mixing withthe first local oscillator signal, iii. a second mixer for mixing thesecond local oscillator signal with the incoming signal providingthereby a second mixer output comprised of the upper high frequencysignal spectrum of interest above F_(LO) and the lower high frequencyspectrum of interest below F_(LO) translated to the near-basebandpassband by mixing with the second-local oscillator signal, iv. a firstfilter for providing a first filter output by limiting the frequencyspectrum of the first mixer output, and v. a second filter for providinga second filter output by limiting the frequency spectrum of the secondmixer output; and b. a digital portion includingi. a first analog-todigital converter for providing a first converter output comprised ofthe first filter output converted from analog to digital format, and ii.a second analog-to-digital converter for providing a second converteroutput comprised of the output of the second filter converted fromanalog to digital format;wherein the digital portion is adapted andarranged to (1) correct phase errors and amplitude between the firstconverter output and the second converter output and combine the firstand second converter outputs to provide an image-rejected signal withinthe near-baseband passband by substantially rejecting the near-basebandimage of a selectable one of the upper high frequency spectrum ofinterest and the lower high frequency spectrum of interest, and (2)translate a selected portion of said near-baseband image-rejected signalto baseband, and wherein the local oscillator is a coarse-tunable localoscillator having a step size S and where the near-baseband passbandextends from F₁ -F_(A) to F₂ +F_(A) and F₁ =k·(F₂ -F₁) where F₁ is afirst frequency, F₂ is a second frequency, k is a positive integer, andF_(A) is a given frequency adjustment, and where S=2·(F2-F1), andwherein said first and second analog-to-digital converters sample theoutput of the first and second bandpass filters at a sampling rateR_(A/D).
 2. The device of claim 1 wherein the digital portion includes atype III Hilbert transform on one of the first and second converteroutputs.
 3. The device of claim 2 wherein the type III Hilbert transformis modified to produce a phase delay of 90 degrees plus a variable phasecorrection.
 4. The device of claim 2 wherein the type III Hilberttransform receives samples at a sampling rate R and the near-basebandpassband is centered at about R/4.
 5. The device of claim 4 whereinR_(A/D) =R.
 6. The device of claim 4 wherein R=R_(A/D) /M and whereinthe first and second converter outputs are subjected to a first digitalfiltering and first decimation before the type III Hilbert transform,the first decimation being by a factor of M, the first digital filteringhaving stopbands at frequencies which would alias into the near-basebandpassband at the sample rate R.
 7. The device of claim 6 wherein thefirst digital filtering has stopbands only at frequencies which wouldalias into the near-baseband passband at the sample rate R.
 8. Thedevice of claim 4 wherein k=1.
 9. The device of claim 1 adapted toreceive a channelized signal spectrum having channel spacing offrequency C and wherein F₂ -F₁ =C·N and N is the number of channels thatfit simultaneously within the near-baseband passband, whereby everychannel of the channelized signal spectrum is translatable to thenear-baseband passband by a unique local oscillator frequency, andeither of two different sets of N channels is selectably providable inthe image-rejected signal for each local oscillator frequency byselectably rejecting the near-baseband image of one of the upper highfrequency spectrum of interest and the lower high frequency spectrum ofinterest.
 10. The device of claim 9 wherein F_(A) =(1/2)·(W-C+W_(ft))where W is the bandwidth of the channels to be received and W_(ft) isthe width of any fine-tuning provided in the digital portion.
 11. Thedevice of claim 1 adapted to receive a channelized signal spectrumhaving channel spacing of frequency C and wherein F₂ -F₁ =C·(N-1) and Nis the number of channels that fit simultaneously within thenear-baseband passband, whereby every channel of the channelized signalspectrum is translatable to the near-baseband passband by a localoscillator frequency, and either of two different sets of N channels isselectably providable in the image-rejected signal for each localoscillator frequency by selectably rejecting the near-baseband image ofone of the upper high frequency spectrum of interest and the lower highfrequency spectrum of interest.
 12. The device of claim 11 wherein F_(A)=(1/2)·(W+W_(ft)) where W is the bandwidth of the channels to bereceived and W_(ft) is the width of any fine-tuning provided in thedigital portion.
 13. The device of claim 1 wherein the desired portionof said near baseband image-rejected signal has a center frequencylocated within an essentially continuous tuning range of the digitalportion of the device, said tuning range extending at least from F₁ toF₂ and wherein F_(A) equals one-half the bandwidth of the signals to bereceived.
 14. The device of claim 13 wherein k=1.
 15. The device ofclaim 1 wherein the desired portion of said near baseband image-rejectedsignal has a center frequency located within an essentially continuoustuning range of the digital portion of the device, said tuning rangeextending at least from F₁ to F₂ and wherein F_(A) equals one-half thebandwidth of the signals to be received plus a hysteresis amount F_(H).16. The device of claim 1 wherein an upper stopband of the first andsecond filters begins at a frequency F_(usb) such that F_(usb) ≦R_(A/D)-(k+1)·S/2-F_(A).
 17. The device of claim 16 wherein F_(usb) =R_(A/D)-(k+1)·S/2-F_(A).
 18. A device for effecting frequency translation andselection of a signal of interest, said device comprising:a. an analogportion includingi. a local oscillator for providing a first localoscillator signal having a frequency F_(LO) and a second localoscillator signal having the frequency F_(LO) approximately inquadrature to the first local oscillator signal, ii. a first mixer formixing the first local oscillator signal with an incoming signalproviding thereby a first mixer output comprised of an upper highfrequency signal spectrum of interest above F_(LO) and a lower highfrequency spectrum of interest below F_(LO) both translated to anear-baseband passband by mixing with the first local oscillator signal,iii. a second mixer for mixing the second local oscillator signal withthe incoming signal providing thereby- a second mixer output comprisedof the upper high frequency signal spectrum of interest above F_(LO) andthe lower high frequency spectrum of interest below F_(LO) translated tothe near-baseband passband by mixing with the second-local oscillatorsignal, iv. a first filter for providing a first filter output bylimiting the frequency spectrum of the first mixer output, and v. asecond filter for providing a second filter output by limiting thefrequency spectrum of the second mixer output; and b. a digital portionincludingi. a first analog-to digital converter for providing a firstconverter output comprised of the first filter output converted fromanalog to digital format, and ii. a second analog-to-digital converterfor providing a second converter output comprised of the output of thesecond filter converted from analog to digital format;wherein thedigital portion is adapted and arranged to (1) correct phase errors andamplitude between the first converter output and the second converteroutput and combine the first and second converter output to provide animage-rejected signal within the near-baseband passband by substantiallyrejecting the near-baseband image of a selectable one of the upper highfrequency spectrum of interest and the lower high frequency spectrum ofinterest, and (2) translate a selected portion of said near-basebandimage-rejected signal to baseband, and wherein the digital portionincludes a variable bandpass decimating filter for selecting the desiredportion of said near-baseband image-rejected signal and translating thedesired portion to within R_(D) /2 of baseband where R_(D) is the outputsampling rate of the variable bandpass decimating filter.
 19. The deviceof claim 18 wherein the incoming signal is an intermediate frequencysignal produced by analog mixing.
 20. The device of claim 18 adapted totransmit as well as receive a high frequency signal of interest.
 21. Adevice for effecting frequency translation and selection of a signal ofinterest, said device comprising:a. an analog portion includingi. alocal oscillator for providing a first local oscillator signal having afrequency F_(LO) and a second local oscillator signal having thefrequency F_(LO) approximately in quadrature to the first localoscillator signal, ii. a first mixer for mixing the first localoscillator signal with an incoming signal providing thereby a firstmixer output comprised of an upper high frequency signal spectrum ofinterest above F_(LO) and a lower high frequency spectrum of interestbelow F_(LO) both translated to a near-baseband passband by mixing withthe first local oscillator signal, iii. a second mixer for mixing thesecond local oscillator signal with the incoming signal providingthereby a second mixer output comprised of the upper high frequencysignal spectrum of interest above F_(LO) and the lower high frequencyspectrum of interest below F_(LO) translated to the near-basebandpassband by mixing with the second local oscillator signal, iv. a firstfilter for providing a first filter output by limiting the frequencyspectrum of the first mixer output; and v. a second filter for providinga second filter output by limiting the frequency spectrum of the secondmixer output; and b. a digital portion includingi. a first analog-todigital converter for providing a first converter output comprised ofthe first filter output converted from analog to digital format, and ii.a second analog-to-digital converter for providing a second converteroutput comprised of the output of the second filter converted fromanalog to digital format;wherein the digital portion is adapted andarranged to (1) correct phase errors and amplitude between the firstconverter output and the second converter output and combine the firstand second converter outputs to provide an image-rejected signal withinthe near-baseband passband by substantially rejecting the near-basebandimage of a selectable one of the upper high frequency spectrum ofinterest and the lower high frequency spectrum of interest, and (2)translate a selected portion of said near-baseband image-rejected signalto baseband, and wherein the digital portion includes a variablebandpass decimating filter for selecting the desired portion of saidnear-baseband image-rejected signal and translating the desired portionto within R_(D) /2 of baseband where R_(D) is the output sampling rateof the variable bandpass decimating filter, and wherein the digitalportion further includes a complex multiplier for rotating to basebandthe output of the variable bandpass decimating filter.
 22. A device foreffecting frequency translation and selection of a signal of interesthaving a maximum bandwidth W, said device comprising:a. an analogportion includingi. a tunable local oscillator for providing a firstlocal oscillator signal at a frequency F_(LO) and a second localoscillator signal at the frequency F_(LO) approximately in quadrature tothe first local oscillator signal, ii. a first mixer for mixing thefirst local oscillator signal with an incoming signal providing therebya first mixer output comprised of an upper high frequency signalspectrum of interest above F_(LO) and a lower high frequency spectrum ofinterest below F_(LO) both translated to a near-baseband passband bymixing with the first local oscillator signal, iii. a second mixer formixing the second local oscillator signal with the incoming signalproviding thereby a second mixer output comprised of the upper highfrequency signal spectrum of interest above F_(LO) and the lower highfrequency spectrum of interest below F_(LO) translated to thenear-baseband passband by mixing with the second local oscillatorsignal, iv. a first filter for providing a first filter output bylimiting the frequency spectrum of the second mixer output; and v. asecond filter for providing a second filter output by limiting thefrequency spectrum o the second mixer output; and b. a digital portionincludingi. a first analog-to-digital converter for providing a firstconverter output comprised of the first filter output converted fromanalog to digital format, ii. a second analog-to-digital converter forproviding a second converter output comprised of the second filterconverted from analog to digital format, iii. a variable phase delaytype III Hilbert transform in a signal path following the firstconverter output, iv. an allpass filter in a signal path following thesecond converter output having a nominal group delay equal to a groupdelay of the type III Hilbert transform, v. an adder for combining theoutput of the type III Hilbert transform with the output of the all-passfilter to provide an image-rejected signal within the near-basebandpassband by substantially rejecting the near-baseband image of aselected one of the upper high frequency spectrum of interest and thelower high frequency spectrum of interest, and vi. a digital fine-tuningdevice having a near-baseband tuning range extending from a lowerfrequency F₁ to an upper frequency F₂ for selecting the desired signalof interest from within the image-rejected signal and translating saidsignal of interest to baseband;wherein F₁ =k·(F₂ -F₁) where k is apositive integer, and R=(F₁ +F₂), where R is the sampling rate ofsignals entering the type III Hilbert transform and the allpass filter,and wherein the near-baseband passband extends from about F₁ -W/2 toabout F₂ +W/2, whereby only the middle of the Nyquist frequency rangerelative to R is employed as a passband during digital processing beforeand through the Hilbert transform.
 23. The device of claim 22 whereink=1.
 24. The device of claim 22 wherein the first and secondanalog-to-digital converters are delta-sigma modulators each of whichsample the respective output of first and second filters at a rate equalto M·R, and wherein the delta-sigma modulators are each followed by adecimating filter with a decimation factor of M.
 25. The device of claim24 wherein the delta-sigma modulators are third-order.
 26. The device ofclaim 22 wherein said selected portion comprises a portion of thefrequency spectrum of the near-baseband passband and wherein correctionof phase and amplitude errors is optimized for image rejection atfrequencies corresponding to the selected portion.
 27. A method oftuning radio frequency signal of interest comprising the steps of:(a)subjecting the radio frequency signal to continuous-time quadraturemixing to produce I and Q signals in approximate quadrature relationshipcontaining the signal of interest within a near-baseband passband; (b)converting said I and Q signals to digital I and Q signals (c)correcting errors between the digital I and Q signals and combining thedigital I and Q signals so as to substantially reject an undesiredmixing image,wherein the continuous-time quadrature mixing is performedby mixing with a signal from a coarse-tunable local oscillator tunablein steps of size S, and wherein the near-baseband passband includes afrequency range extending from a lower frequency F₁ -F_(A) to an upperfrequency F₂ +F_(A), where F₁ is a first frequency, F₂ is a secondfrequency, and F_(A) is a given frequency adjustment, and whereinF1=k·(F₂ -F₁) where k is a positive integer, and wherein S=2·(F₂ -F₁).28. The method of claim 27 wherein F_(A) =(1/2)·(W-C+W_(ft)) where W isthe bandwidth of channelized signals to be received from a channelizedspectrum with channel spacing C, and where W_(ft) is the width of anyfine-tuning performed in the step of selecting the signal of interestfrom the near-baseband passband and translating the signal of interestto baseband.
 29. The method of claim 27 wherein F_(A) =W/2 wherein W isthe maximum bandwidth of signals desired to be received.
 30. The methodof claim 27 wherein F_(A) =W/2+F_(H) wherein W is the maximum bandwidthof signals desired to be received and F_(H) is a hysteresis amount. 31.The method of claim 27 wherein the step of selecting the signal ofinterest from the near-baseband passband and translating the signal ofinterest to baseband comprises translating the signal of interest tobaseband by frequency translation.
 32. A method of tuning a radiofrequency signal of interest comprising the steps of:(a) subjecting theradio frequency signal to continuous-time quadrature mixing to produce Iand Q signals in approximate quadrature relationship containing thesignal of interest within a near-baseband passband; (b) converting saidI and Q signals to digital I and Q signals (c) correcting errors betweenthe digital I and Q signals and combining the digital I and Q signals soas to substantially reject an undesired mixing image,wherein the step ofcombining the I and Q signals comprises: subjecting one of said I and Qsignals to filtration by a variable phase change type III Hilberttransform; and subjecting the other signal to an allpass filter havingthe same nominal group delay as the variable phase change type IIIHilbert transform.
 33. The method of claim 32 wherein the near-basebandpassband is centered at about R/4 where R is the sampling rate ofsignals entering the Hilbert transform and the allpass filter.
 34. Themethod of claim 33 wherein R_(A/D) =R.
 35. The method of claim 33wherein the step of converting said I and Q signals to digital signalsis performed by delta-sigma modulators, and where R=R_(A/D) /M, where Mis the decimation ratio of a digital filtering and decimation processperformed before the Hilbert transform and allpass filter and after theanalog to digital conversion, the filtering portion of which processsubstantially rejects all frequencies not rejected by thecontinuous-time filtering step which would alias into the near-basebandpassband at the sampling rate R.
 36. The method of claim 32 furtherincluding the step of first subjecting a signal to continuous-timemixing to an intermediate frequency to produce a signal which is thensubjected to the remaining steps of the method.
 37. A method of tuning aradio frequency signal of interest comprising the steps of:(a)subjecting the radio frequency signal to continuous-time quadraturemixing to produce I and Q signals in approximate quadrature relationshipcontaining the signal of interest within a near-baseband passband; (b)converting said I and Q signals to digital I and Q signals (c)correcting errors between the digital I and Q signals and combining thedigital I and Q signals so as to substantially reject an undesiredmixing image,wherein the step of translating the signal of interest tobaseband is performed by a variable bandpass digital filtering anddecimation process utilizing aliasing to alias the signal of interest towithin R_(D) /2 of baseband where R_(D) is the sampling rate at theoutput of the variable bandpass digital filtering and decimationprocess, followed by digital quadrature mixing including multiplicationby complex coefficients to rotate the signal of interest from withinR_(D) /2 of baseband to baseband.
 38. A device for effecting frequencytranslation and selection of a signal of interest, said devicecomprising:a. an analog portion includingi. a local oscillator forproviding a first local oscillator signal having a frequency F_(LO) anda second local oscillator signal having the frequency F_(LO)approximately in quadrature to the first local oscillator signal, ii. afirst mixer for mixing the first local oscillator signal with anincoming signal providing thereby a first mixer output comprised of anupper high frequency signal spectrum of interest above F_(LO) and alower high frequency spectrum of interest be low F_(LO) both translatedto a near-baseband passband by mixing with the first local oscillatorsignal, iii. a second mixer for mixing the second local oscillatorsignal with the incoming signal providing thereby, a second mixer outputcomprised of the upper high frequency signal spectrum of interest aboveF_(LO) and the lower high frequency spectrum of interest below F_(LO)translated to the near-baseband passband by mixing with the second localoscillator signal, iv. a first filter for providing a first filteroutput by limiting the frequency spectrum of the first mixer output, andv. a second filter for providing a second filter output by limiting thefrequency spectrum of the second mixer output; and b. a digital portionincludingi. a first analog-to digital converter for providing a firstconverter output comprised of the first filter output converted fromanalog to digital format, and ii. a second analog-to-digital converterfor providing a second converter output comprised of the output of thesecond filter converted from analog to digital format;wherein thedigital portion is adapted and arranged to (1) correct phase errors andamplitude between the first converter output and the second converteroutput and combine the first and second converter outputs to provide animage-rejected signal within the near-baseband passband by substantiallyrejecting the near-baseband image of a selectable one of the upper highfrequency spectrum of interest and the lower high frequency spectrum ofinterest, and (2) translate a selected portion of said near-basebandimage-rejected signal to baseband, and wherein the digital portionincludes a variable phase change type III Hilbert transform on one ofthe first and second converter outputs, and an allpass filter having thesame nominal group delay as the variable phase change type III Hilberttransform on another of the first and second converter outputs.
 39. Thedevice of claim 38 wherein the type III Hilbert transform is modified toproduce a phase delay of 90 degrees plus a variable phase correction.40. The device of claim 1 wherein the digital portion is adapted andarranged to translate a selected portion of said near-basebandimage-rejected signal to baseband by frequency translation.
 41. A tunercomprising:(a) a quadrature mixer responsive to an RF signal so as toproduce therefrom in-phase and quadrature signals in approximatequadrature relation containing both a desired signal and an undesiredmixing image,(i) the desired signal being within a first one of (1) apositive frequency range and (2) a negative frequency range, (ii) theundesired mixing image being within a second one of (1) the positivefrequency range and (2) the negative frequency range, the second onebeing different from the first one; and (b) a digital signal processingdevice coupled to the quadrature mixer so as to receive the in-phase andquadrature signals wherein the digital signal processing device isstructured and arranged so as to both(i) correct errors between thein-phase and quadrature signals and (ii) combine the in-phase andquadrature signals so as to substantially reject the undesired mixingimage,wherein the digital signal processing device includes a variablebandpass decimating filter for selecting a desired portion of thecombined in-phase and quadrature signals and translating the desiredportion to within R_(D) /2 of baseband where R_(D) is the outputsampling rate of the variable bandpass decimating filter.
 42. The tunerof claim 41, wherein the digital signal processing device is structuredand arranged to correct phrase errors between the in-phase andquadrature signals by changing the relative phase relationship betweenthe in-phase and quadrature signals so as to place an undesiredquadrature phasor into phase opposition with a corresponding in-phasephasor, regardless of the resulting phase relationship of a desiredquadrature phasor the corresponding in-phase phasor, and wherein thedigital signal processing device further includes a complex multiplierfor rotating to baseband the output of the variable bandpass decimatingfilter.